can some1 help plz?A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10m greater than the other side. Find the length of the fence needed to surround this garden if the area of the vegetable garden is 2184m2.

Accepted Solution

Answer:The length of the fence needed to surround this garden is [tex]188\ m[/tex]Step-by-step explanation:Letx----> the length of the rectangular fencey----> the width of the rectangular fencewe know that the area of the rectangular fence is equal to[tex]A=xy[/tex][tex]A=2,184\ m^{2}[/tex]so[tex]2,184=xy[/tex] -----> equation Awe have [tex]x=10+y[/tex] -----> equation BSubstitute equation B in equation A[tex]2,184=(10+y)y[/tex][tex]y^{2}+10y-2,184=0[/tex]using a graphing toolsolve the quadratic equationThe solution is [tex]y=42\ m[/tex]see the attached figureFind the value of x[tex]x=10+y[/tex] ----> [tex]x=10+42=52\ m[/tex] Find the perimeter of the rectangular fenceThe perimeter is equal to[tex]P=2(x+y)[/tex]substitute the values[tex]P=2(52+42)=188\ m[/tex]